Analysis of Vortex Tube Applications in Hydrogen Liquefaction
Transcript of Analysis of Vortex Tube Applications in Hydrogen Liquefaction
Analysis of Vortex Tube Applications in Hydrogen Liquefaction
Marshall Crenshaw
Washington State UniversityPullman, WANovember 14, 2017
• >80% of global energy comes from fossil fuels.1
• Since 1976, global temperatures warmer than long-term average.2
• 11 of the top 12 hottest years are from 2003-2016.3
Why is Renewable Energy Necessary?
1 International Energy Agency Technical Report. Key World Energy Statistics. 2016 2 https://climate.nasa.gov/scientific-consensus/3 https://www.ncdc.noaa.gov/sotc/global/201613
• 9th most abundant element in earth’s crust
• Photo-biological bacteria produce hydrogen
H2 Production
http://www.fsec.ucf.edu/en/consumer/hydrogen/basics/images/HydrogenProductionPaths.gif
• Lowest volumetric density
• Containers are pressurized or cryogenic to increase density
Difficulties of H2
https://energy.gov/eere/fuelcells/hydrogen-storage
• Double density when liquefying over pressurizing
Liquid vs Pressurized H2
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Den
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m³)
Pressure of Compressed Hydrogen (MPa)
Pressurized Hydrogen
Liquid Hydrogen
Pressurized Tank @ 70 MPa
Pressurized Tank @ 35 MPa
• Inexpensive cooling device
• 1 high pressure stream 2 low pressure streams
• Transfers cold stream energy hot outer stream
• No moving parts
Diagram of Vortex Tube (VT)
• Low-cost cycle for hydrogen liquefaction
• Low-efficiency method for liquefaction
• Increase cycle efficiency by adding component
Pre-cooled Linde-Hampson Cycle
• Additional compressor and heat exchanger
• Cycle efficiency: Adding compressor > Adding throttle
• 3rd HX reduces O-P ratio of hydrogen
• What is O-P ratio?
Pre-cooled L-H cycle with VT
• Equilibrium O-P ratio depends on temperature of hydrogen
• Normal hydrogen 3:1 O-P ratio
• Liquid hydrogen all parahydrogen
• Catalyst added to HXs to maintain equilibrium O-P ratio
• Why is equilibrium hydrogen important?
Orthohydrogen & Parahydrogen
https://3c1703fe8d.site.internapcdn.net/newman/gfx/news/hires/2011/1-nuclearmagne.jpg
• 50% of normal hydrogen boils away in 200 hours
Importance of Ortho-Para Equilibrium
Gursu, S. et al. An Optimization Study of Liquid Hydrogen Boil-Off Losses,Int. J. Hydrogen Energy., v. 17, p. 227, 1992.
Statistical Thermodynamic Properties of H2
https://3c1703fe8d.site.internapcdn.net/newman/gfx/news/hires/2011/1-nuclearmagne.jpg
Stat Thermo
https://hydrogen.wsu.edu/2015/06/22/why-equilibrium-hydrogen-doesnt-exist/
REFPROP
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Idea
l-gas
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halp
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Temperature [K]
Ortho [REFPROP]
Para [REFPROP]
REFPROP with Corrected Orthohydrogen vs. Stat Thermo
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Para [REFPROP]
Stat Thermo
MATLAB
https://hydrogen.wsu.edu/2015/06/22/why-equilibrium-hydrogen-doesnt-exist/
r2 = 0.999996
Equilibrium Ofrac
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libriu
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Temperature (K)
Piece-Wise Equilibrium H2 Function
Coefficients of equilibrium MATLAB function
a1 1.935x10-4 b1 -2.044 c1 1.111x10-7
a2 -5.832x10-3 b2 -2.724x10-2 c2 -2.243x10-6
a3 3.448x10-2 b3 0.75 c3 -1.886x10-5
c4 6.514x10-4
c5 -3.499x10-3
Ofrac =
a1T2 + a2T + a3 T ≤ 24.82Kb1eb2T + b3 T ≤ 51.51K
�i=1
4
ciTi + c5 T > 51.51K
Approximate Equilibrium O-P Function
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libriu
m O
rthoh
ydro
gen
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Temperature (K)
Stat ThermoMATLAB
r2 = 0.99986
Liquefaction Components & Cycle Assumptions
• Bath pressure is atmospheric (101.3 kPa) and temperature is 77 K
• LN2 Bath is catalyzed: Ofrac = ~0.5
• Heat extracted:
�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵 = �̇�𝑚𝐻𝐻2 ℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑖𝑖𝑖𝑖 − ℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑜𝑜𝑜𝑜𝐵𝐵 + Δℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐
• Added work to hydrogen liquefaction:
�̇�𝑊𝐵𝐵𝐵𝐵𝐵𝐵𝐵 =�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵 �
𝐿𝐿𝐿𝐿2𝑖𝑖𝑖𝑖𝑖𝑖𝐵𝐵𝑖𝑖𝐿𝐿𝐿𝐿2𝐹𝐹𝐹𝐹𝐹𝐹
�̇�𝑚𝐿𝐿𝐻𝐻2 � Δ𝐻𝐻𝑐𝑐𝐵𝐵𝑣𝑣,𝑁𝑁2
LN2 Bath
𝐿𝐿𝐿𝐿2 𝐵𝐵𝐵𝐵𝐵𝐵ℎ
• Energy balance equation:
�𝑖𝑖=1
𝑖𝑖
∆ℎ𝑖𝑖 + ∆ℎ𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐,𝑖𝑖 = 0
• Minimum temperature approach solves for outlet temperatures
• Hot stream T limit: 𝑇𝑇𝐻𝐻𝑜𝑜𝐵𝐵,𝑜𝑜𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝐵𝐵 = Δ𝑇𝑇𝑙𝑙𝑖𝑖𝑖𝑖 + 𝑇𝑇𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖𝑖𝑖𝐶𝐶𝐵𝐵,𝑖𝑖𝑖𝑖
• Cold streams T limit: 𝑇𝑇𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝐵𝐵 = 𝑇𝑇𝐻𝐻𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖 − Δ𝑇𝑇𝑙𝑙𝑖𝑖𝑖𝑖
Counter-flow Heat Exchanger
𝐻𝐻𝐻𝐻3
Cold
Nitrogen𝐻𝐻𝐻𝐻2
Hot𝐻𝐻𝐻𝐻4
• Staging compressors decreases their work
• 4 stages is optimal for compressors
Staged Compression with Intercooling
• Pressure Ratio per stage: 𝑃𝑃𝑃𝑃𝐶𝐶𝐵𝐵𝐵𝐵𝑠𝑠𝑖𝑖 =𝑛𝑛
�𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜𝑃𝑃𝑖𝑖𝑛𝑛
• Enthalpy of compressor: ℎ2 = 𝐵𝑠𝑠−𝐵1𝜂𝜂𝐶𝐶
+ ℎ1
• Work of compressor: 𝐿𝐿𝑐𝑐 = ∑𝑖𝑖=1𝑖𝑖 �̇�𝑚𝐶𝐶 ℎ2,𝑖𝑖 − ℎ1,𝑖𝑖
• Heat extracted: �̇�𝑄𝐶𝐶 = 𝐿𝐿𝑐𝑐 + ∑𝑖𝑖=1𝑖𝑖 ℎ𝑖𝑖 − ℎ𝑖𝑖−1
• Enthalpy of expander: ℎ2 = 𝜂𝜂𝐸𝐸 ℎ1 − ℎ𝐶𝐶 + ℎ1
Compressor/Expander Component
𝐶𝐶
𝐿𝐿𝐶𝐶
�̇�𝑄𝐶𝐶
𝐿𝐿𝐸𝐸
𝐸𝐸
• Throttle is ideally isenthalpic: ℎ𝑖𝑖𝑖𝑖 = ℎ𝑜𝑜𝑜𝑜𝐵𝐵• Quality of LH2: solved with enthalpy & pressure
• Heat of O-P conversion in tank:�̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐 = �̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑖𝑖𝑖𝑖∆ℎ𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐
• Return stream flow:�̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑜𝑜𝑜𝑜𝐵𝐵 = �̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑖𝑖𝑖𝑖 � X𝐻𝐻2 +
�̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐 + �̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝐵𝑖𝑖𝐵𝐵𝐵𝐵 𝑖𝑖𝑖𝑖𝐵𝐵𝑇𝑇
ℎ𝐿𝐿𝐻𝐻,𝐻𝐻2
Throttle & Tank
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝐻𝐻2 𝑇𝑇𝐵𝐵𝑇𝑇𝑇𝑇
𝐽𝐽𝑇𝑇
• Specific exergy: 𝐻𝐻1 = ℎ0 − ℎ1 − 𝑇𝑇0 𝑠𝑠0 − 𝑠𝑠1
• Exergy destruction: ∆𝐻𝐻𝐷𝐷𝑖𝑖𝐶𝐶𝐵𝐵= � �̇�𝑚𝑖𝑖𝑖𝑖𝐻𝐻𝑖𝑖𝑖𝑖 −� �̇�𝑚𝑜𝑜𝑜𝑜𝐵𝐵𝐻𝐻𝑜𝑜𝑜𝑜𝐵𝐵 −𝑊𝑊
• Limits are set to the exergy destruction of throttle (lower) and expander (higher)
Effectiveness of a VT
• Exergy destruction of devices:∆𝐻𝐻𝑉𝑉𝑇𝑇= �̇�𝑚𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖𝐻𝐻𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 − �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵𝐻𝐻𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵
∆𝐻𝐻𝐽𝐽𝑇𝑇= �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐽𝐽𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 + �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐽𝐽𝑇𝑇,𝐵𝑜𝑜𝐵𝐵
∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣
= �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 − 𝑊𝑊𝐸𝐸𝐸𝐸𝑣𝑣,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 + �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣,𝐵𝑜𝑜𝐵𝐵 − 𝑊𝑊𝐸𝐸𝐸𝐸𝑣𝑣,𝐵𝑜𝑜𝐵𝐵
• Exergy destruction using effectiveness• ∆𝐻𝐻𝑉𝑉𝑇𝑇= ∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣 + 1 − 𝜀𝜀𝑉𝑉𝑇𝑇 ∆𝐻𝐻𝐽𝐽𝑇𝑇 − ∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣
Effectiveness of a VT cont.
• Cold fraction: 𝑉𝑉𝑇𝑇𝑐𝑐𝑐𝑐 = �̇�𝑙𝑉𝑉𝑉𝑉,𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐�̇�𝑙𝑉𝑉𝑉𝑉,𝑖𝑖𝑛𝑛
• Pressure Ratio: 𝑉𝑉𝑇𝑇𝑃𝑃𝑃𝑃 = 𝑃𝑃𝑖𝑖𝑛𝑛𝑃𝑃𝑉𝑉𝑉𝑉,𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐
• Hot outlet Pressure: 𝑃𝑃𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 = ⁄1 3 𝑃𝑃𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 + ⁄2 3 𝑃𝑃𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖
• Outlet temperatures are solved with effectiveness
Variables of the VT
Cycle Parameters
Previous Cycle Parameters
Cycle Analysis & Results
• Liquid hydrogen yield: 𝜑𝜑 = �̇�𝑙𝑓𝑓
�̇�𝑙
• Ratio of nitrogen to compressed hydrogen flow: 𝜓𝜓 =�̇�𝑙𝑁𝑁2�̇�𝑙
• Liquid yield maximum: 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸 = 𝐵9−𝐵4𝐵9−𝐵7
• Relating 𝜓𝜓 to 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸: 𝜓𝜓 = 𝐵1−𝐵2𝐵11−𝐵10
+ 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸𝐵7−𝐵1𝐵11−𝐵10
State-Point Analysis of Ideal Cycle
Peschka W. Liquid hydrogen: fuel of the future. Springer Science & Business Media; 2012 Dec 6.
• O-P conversion happens at LN2 Bath and LH2 tank
• �̇�𝑚𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖 = �̇�𝑄𝑉𝑉𝑇𝑇𝑛𝑛𝑇𝑇𝐵𝑔𝑔−𝐵𝑓𝑓
• �̇�𝑚∗ = �̇�𝑚 + �̇�𝑙𝑏𝑏𝑜𝑜𝑖𝑖𝑐𝑐𝜑𝜑𝑚𝑚𝑇𝑇𝑚𝑚
• 𝜑𝜑∗ = �̇�𝑙𝑓𝑓
�̇�𝑙∗= 𝜑𝜑𝑚𝑚𝑇𝑇𝑚𝑚
1+ ��̇�𝑄𝑉𝑉𝑇𝑇𝑛𝑛𝑇𝑇 �̇�𝑙𝑓𝑓 𝐵8−𝐵7
• 𝜓𝜓∗ =�̇�𝑙𝑁𝑁2�̇�𝑙∗
O-P conversion at LH2 Tank
• Maximum yield of LN2 Bath: 𝜑𝜑𝑁𝑁2,𝑙𝑙𝐵𝐵𝐸𝐸 =�̇�𝑙𝑁𝑁2,𝑓𝑓
�̇�𝑙𝑁𝑁2= 𝐵𝑁𝑁,1−𝐵𝑁𝑁,2
𝐵𝑁𝑁,1−𝐵𝑁𝑁,5
• Work of LN2 Bath: 𝛼𝛼 = 1𝜑𝜑
�̇�𝑊�̇�𝑙 𝑐𝑐𝑜𝑜𝑙𝑙𝑣𝑣
• Work of compressor: �̇�𝑊�̇�𝑙 𝑐𝑐𝑜𝑜𝑙𝑙𝑣𝑣
= 𝑇𝑇𝑖𝑖𝑖𝑖 � 𝑠𝑠𝑖𝑖𝑖𝑖 − 𝑠𝑠𝑜𝑜𝑜𝑜𝐵𝐵 − ℎ𝑖𝑖𝑖𝑖 − ℎ𝑜𝑜𝑜𝑜𝐵𝐵
• 𝛼𝛼𝑁𝑁2 = 1𝜑𝜑𝑁𝑁2,𝑚𝑚𝑇𝑇𝑚𝑚
𝑇𝑇𝑁𝑁,1 � 𝑠𝑠𝑁𝑁,1 − 𝑠𝑠𝑁𝑁,2 − ℎ𝑁𝑁,1 − ℎ𝑁𝑁,2
Work of LN2 Bath
Peschka W. Liquid hydrogen: fuel of the future. Springer Science & Business Media; 2012 Dec 6.
• State-Point work of liquefaction for pre-cooled L-H cycle:
𝛼𝛼𝐻𝐻2 =1𝜑𝜑∗
𝑇𝑇1 � 𝑠𝑠1 − 𝑠𝑠2 − ℎ1 − ℎ2 + 𝛼𝛼𝑁𝑁2 𝜓𝜓∗ +�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵
ℎ12 − ℎ11
• Peak pressure of LN2 Bath: 100 bar (10 MPa)
• Temperature of LN2 Bath: 63.2 K or 77 K
• State-Point work of liquefaction results:- 𝛼𝛼𝐶𝐶,63.2 𝐾𝐾 = 13.65 kWh∙kg-1
- 𝛼𝛼𝐶𝐶,77 𝐾𝐾 = 19.95 kWh∙kg-1
• Peschka value: 𝛼𝛼𝑃𝑃 = 16.27 kWh∙kg-1
State-Point Results
• Work of liquefaction for component-based model:
- 𝛼𝛼𝑐𝑐,63.2 𝐾𝐾 = 14.82 kWh∙kg-1
- 𝛼𝛼𝑐𝑐,77 𝐾𝐾 = 20.83 kWh∙kg-1
• Percentage error between results:
- 63.2 K: 8.57%
- 77 K: 4.41%
• Error caused by heat exchanger and LN2 components
State-Point vs. Component Results
Vortex Tube Simulation
Reduced Work for L-H w/VT Cycle
Cycle Analysis & Results
Simulation of L-H w/VT Cycle
• Simulate higher complexity cycles e.g. pre-cooled Claude
• Vary the LN2 Bath temperature to 63.2 K
• Higher inlet pressure tests for vortex tube
• Continued tests of vortex tube catalyzation
• Test vortex tube as a final liquefaction component
Recommendations
• Simplified Statistical thermodynamic models created
• Variable components created for the pre-cooled L-H cycle
• Component model verified with state-point model
• Effectiveness introduced as a new VT variable
• Required effectiveness provided for combinations of 𝑉𝑉𝑇𝑇𝑐𝑐𝑐𝑐 and 𝑉𝑉𝑇𝑇𝑃𝑃𝑃𝑃 values
Summary